A linear displacement transducer of this type is shown in my previous U.S. Pat. No. 4,667,158 and is illustrated in FIG. 1. The transducer is a helical coil 2 of an electrical conductor wound at a uniform pitch on cylindrical thin-walled tube or bobbin 1 of an electrical insulator or a poor conductor such as stainless steel. Preferably, the tube also has suitable properties for use as a dry bearing surface, for example Teflon. The helical coil 2 is fixed to the first of two relatively movable bodies for which the relative displacement is to be measured.
A non-ferromagnetic, electrically conducting rod or preferably a tube forms a core 3 which is slidable within the bobbin 1. It is made, for example, of aluminum or copper and is fixed to the second of the two relatively moving bodies.
Preferably the coil is surrounded by a low and constant reluctance path so that changes in coil inductance with respect to core 3 movement is maximized. This is preferably accomplished by positioning a material, such as ferrite 5, having a high magnetic permeability., but low electrical conductivity surrounding the coil. This material provides the desired low magnetic reluctance while not permitting the formation of significant eddy currents and not exhibiting a substantial skin effect.
Preferably this high permeability, low conductivity material is itself surrounded with a tubular shield 4 of high electrical conductivity to confine the field of the coil to the ferrite 5 and the skin layer of the shield 4 and to prevent external fields from linking with the coil 2. The shield 4 confines the magnetic flux generated from stray fields by the current in the coil 2 and shields it over a wide frequency range. It is preferably made of a material having both high electrical conductivity and high magnetic permeability, such as soft iron or low carbon steel.
An AC electrical energy source 6 and a detector circuit means 7, preferably in the form of a bridge circuit, are electrically connected to the coil 2. The AC source 6 operates at a frequency, preferably in the range of 50-200 Khz, which may be designated a carrier frequency f.sub.c. An important key to the efficient and effective operation of a transducer of this type is that the frequency of the source 6 be high enough that the skin depth in the core 3 is substantially less than the radius of the core and less than the thickness of the wall of the tube.
The source 6 drives the coil through a resistor 8 which has a resistance which is much greater than the inductive reactance of the coil and its associated structures so that effectively the transducer is driven by a current source. Therefore, the voltage across the transducer coil 5 is approximately (V/R)*(2 pi f.sub.c L).
The detector circuit 7 detects a signal at an AM detector 9 which is proportional to the inductance of the coil 2 and its associated structures. The coil voltage is proportional to coil inductance, which in turn is proportional to the displacement of the core 3.
In the operation of the basic concept of the displacement measurement apparatus of FIG. 1, the AC source 6 excites the bridge circuit, including the transducer coil 2 in one of its branches Because of the skin effect at the frequency at which the AC source 6 is operating, magnetic fields in the core 3 are confined to a thin layer approximately equal to the sum of the skin depth in the core material which is typically on the order of 0.25 millimeters thick plus the spacing from the exterior of the core 3 to the interior of the coil 2. Because the skin depth is considerably less than the radius of the core, the magnetic flux is confined to a path in the region of the core 3 which has a considerably smaller cross-sectional area than the flux path where there is no core 3. Since reluctance is inversely proportional to the cross-sectional area of the flux path, the core 3 has the effect of substantially increasing the reluctance and therefore substantially reducing the magnetic flux in the region of the core. With the core 3 partially inserted in the coil 2 of the transducer, the interior of the coil 2 can be divided into the region occupied by the core 3 where magnetic flux is low, and the region unoccupied by the core where magnetic flux is relatively high compared to the core region. Therefore, the flux linkages of the coil are substantially reduced as a result of the insertion of the core and are reduced in proportion of the extent of the insertion of the core within the coil 2. This, in turn, proportionally reduces the self inductance of the coil 2. Thus, the movable core varies the self inductance and the impedance and therefore varies the voltage across the transducer in proportion to its displacement.
While a great variety of detector circuits are known to those skilled in the art for detecting a signal which is proportional to the changes in coil inductance or voltage, the detector circuit of FIG. 1 operates well. A bridge is designed to be brought into AC amplitude balance by adjustable resistor 10 when the core 3 is centered within the coil 2. The AC source 6 is a signal at a frequency f.sub.c. The amplitude of the transducer signal at frequency f.sub.c at the node 11 of the bridge is proportional to the displacement of the core 3. The amplitude of the balance signal at frequency f.sub.c at the opposite node 12 is adjusted so that it is equal to the amplitude of the transducer signal at node 11 when the core 3 is centered within the coil 2. A detector circuit means comprising two AM detectors 9A and 9B and a differential amplifier 14 are provided to detect the difference between the modulation amplitudes at the nodes 11 and 12.
The displacement of the core 3 is effectively providing an amplitude modulated signal at the terminal 11, the amplitude of which is proportional to displacement of the core 3 and may be detected by the AM detector 9B to provide an output signal which is directly proportional to the displacement of the core 3. The balance signal at node 12 is detected by an AM detector circuit 9A. The output signals from the two AM detectors 9A and 9B are applied to a differential amplifier 14, the output of which provides a signal V.sub.out which is proportional to the displacement of the core 3. Further details of the basic concept are described in more detail in my above cited U.S. Patent.
One problem with a transducer constructed as described above is that its inductance and therefore the output voltage of the detector means is not exactly proportional to the relative displacement x shown in FIG. 1 of the core 3 into the coil 2. The relative displacement x is measured as the position of the interior end 18 of the core 3 with respect to the right end 24 of the coil 2. If the transducer were operating as an ideal linear transducer, the output voltage signal would be proportional to the displacement x and therefore dV/dx would be constant over the entire length of the coil.
Instead, however, for the simple coil illustrated in FIG. 1, dV/dx decreases as the displacement x increases so that the transfer function, designate V.sub.u (x) in FIG. 3 falls below the ideal linear relationship V.sub.o (x) as x increases. This occurs for two reasons.
The loss in the device of FIG. 1 increases as the core 3 is displaced further into the coil 2. Losses become greater as the core displacement increases because the core itself is relatively lossy and therefore there is more lossy core in the field as the core insertion or displacement x increases.
The non-uniformity of the flux in the transition region 23 adjacent the left end of the core 3 also contributes significantly to this nonlinearity. FIG. 1 illustrates a portion of the flux lines 20 which have a radial component in the transition region 23 of the flux 22 to join the boundaries of the uniform flux on opposite sides of this transition region 23. This transition region produces an end effect which causes an increasing departure from linearity as the displacement of the core 3 increases. The reason the end effects increase as the displacement of the core 3 into the coil 2 increases is that, as the insertion x increases, the transition region 23 occupies an increasingly greater proportion of the segment of the coil 2 which is not occupied by the core 3. There is, of course, no sharp boundary for the transition region. However, we have found that end effects become negligeable within approximately three coil diameters from the end 18 of the core 3. The total departure of the transfer function V.sub.u (x) for the simple, uncompensated coil illustrated in FIG. 1 from the transfer function V.sub.o (x) of an ideal, linear coil is designated as the ERROR in FIG. 3.
It is therefore an object and feature of the present invention to substantially eliminate this error so that transducer displacement becomes a more accurate and precise linear function of core displacement into the coil.
A further object and feature of the invention is to provide such an improvement in a manner which may be economically mass produced.